There exist a wide variety of materials displaying interesting optical properties on a scale ranging from hundreds down to single nanometres. Some examples include viruses, cells, polymer blends, polycrystalline and nanocomposite materials, quantum dots, electronic components such as transistors and memory cells. None of these structures can be directly resolved by conventional optical microscopy due to the resolution limit imposed by the diffraction of light. This limit is formally expressed by Abbe's law (d≈0.5λ/NA) where d is the lateral resolution, λ is the light wavelength and NA numerical aperture of the microscope objective. Similarly, the light cannot be focused to a disk of radius smaller then roughly half the wavelength.
A first way around the diffraction limit was obtained with a spatial confinement of the light source with aperture-type near-field optical microscopes (a-SNOM). This could be realised by opening a small (subwavelength-sized) aperture in an otherwise opaque screen. To avoid the diffraction effects, the sample has to be placed in the immediate vicinity of the aperture. Usually, the intensity of light transmitted through or reflected from the sample is recorded. Phase sensitivity can also be achieved e.g. by sinusoidal phase modulation of the measurement wave (see M. Vaez-Iravani et al. in “Applied Physics Letters” vol. 62, 1993, p. 1044).
The resolution of an a-SNOM is limited by the size of the aperture. The transmission efficiency of a small aperture rapidly decreases with decreasing size to wavelength ratio. This limits the smallest practical aperture sizes to roughly 50 nm for the visible light and to hundreds of nanometres or more for infrared radiation.
To improve the resolution even further, the apertureless or scattering-type near-field microscope (s-SNOM) was developed. In s-SNOM, a sharp, usually metallic tip is dithered in the proximity of the sample and illuminated by the focused light. The light scattered by the tip is collected since it conveys the information on the local optical properties of the sample. The presence of the sample modifies the scattered light amplitude and phase because the scattering depends not only on the tip alone, but on the polarizability of the entire coupled tip-sample system. The optical resolution of s-SNOM is essentially limited only by the tip radius. However, the largest part of the collected light does not originate from the tip apex. Instead, it is mostly produced by reflections and scatterings from the tip shaft and the entire illuminated area of the sample. This undesirable part of the signal, commonly referred to as background light, has to be separated from the measured quantities. Furthermore, to obtain the complex-valued dielectric constant of the sample both the amplitude and phase of the scattered light have to be determined.
The background signal can be avoided by taking advantage of the continuous tip oscillation. The tip dithering induces a periodic change in the coupled tip-sample system polarizability thus a modulation of the scattered wave S representing the signal light. However, the s-SNOM background B is also strongly modulated at the same frequency Ω. The contrasts can be enhanced and scattering source S better distinguished from the background B if the signal is demodulated at a higher harmonic, nΩ, n>1 (see G. Wurtz et al. in “The European Physical Journal —Applied Physics” vol. 5, 1999, 269).
The light intensity In detected by the detector at frequency nΩ, n>0 is in general a complicated sum of all possible signal and background interference products:In=ES,nEB,0 cos(φS,n−φB,0)+ES,0EB,n cos(φS,0−φB,n)+¼Σi≠0,nES,iES,n±i cos(φS,i−φS,n±i)+¼Σi≠0,nEB,i+EB,n±i cos(φB,i−φB,n±i))+½Σi≠0,nEB,iES,n±i cos(φB,i−φS,n±i)where the ES,i and EB,i are the i-th harmonic components of the signal and background amplitudes and the φS,i and φB,0 their corresponding phases. In practice it can be assumed EB,0>>ES,i and also EB,0>>EB,i for every i≧1. For a sufficiently high harmonic n, usually n≧2, we also have EB,n≈0. The detected intensity is then simplyIn=ES,nEB,0 cos(φS,n−φB,0)
However, this method provides no phase information and the measured quantity In is dependent on the amplitudes of the background and the signal and the exact phase relation between them.
By combining the higher harmonic demodulation with an interferometric detection, the contribution of the background can be significantly reduced as the signal in this case contains one additional term, representing the interference product between the source S and the reference wave R:In=ES,n(EB,0 cos(φS,n−φB,0)+ER cos(φS,n−φR))
Usually the reference (ER) term is dominant. By effectively neglecting the background contribution (EB,0<<ER) it was proposed by Taubner et al. (“Journal of Microscopy” vol. 210, 2003, p. 311) to reconstruct the amplitude and phase by measuring the signal twice (yielding signal amplitudes s1 and s2), with 90° reference phase shift between the measurements. With the known detector sensitivity a, the n-th harmonic amplitude ES,n and phase φS,n of the scattered waves are then reconstructed as:ES,n=sqrt(s12+s22)/(aER)φS,n=arctan(s1,s2)
In a typical s-SNOM experiment of the above type using infrared light with wavelength around 10 μm, the reference to background amplitude ratio ER:EB ranging from 3 to 10 is observed. In an average case of ER:EB=5 the above expressions lead to an error of up to 28% in the calculated amplitude ES,n and up to 17° in the phase φS,n compared to the exact values. Further, EB,0 is unknown and generally not constant thus introducing artificial optical contrasts.
Finally, the adjustment of the interferometer is usually performed with a fixed reference phase. This often results in suboptimal alignment since the maximum in the detected intensity doesn't necessarily maximize the real signal amplitude, but only its projection on the reference wave (cosine component). It is therefore advantageous to measure the amplitude and phase simultaneously.
Phase sensitivity can also be achieved through an interferometric method proposed by Zenhausern et al. (EP 757 271). There it is also assumed that interferometric detection will enhance the detected signal intensity by several orders of magnitude by detecting a signal proportional to (k r)3 instead of (k r)6 in the Rayleigh scattering limit k r<<1, where k is the wave vector of the illuminating light and r is the radius of the scatterer. However, this assumption would only be correct in the absence of the background signal, which in reality amplifies the measured scattering signal the same way an interferometric reference does. As explained above, the additional amplification due to the interferometric detection is usually only a factor 10 or less over the background. In EP 757 271, this effect was not considered and consequently no way to eliminate the background contribution was proposed.
The first and so far the only method capable of both the background interference elimination and simultaneous amplitude and phase measurement was introduced by Hillenbrand et al. (DE 100 35 134). This method is based on the detection of scattering at higher harmonics nΩ of the tip dithering frequency, heterodyned with the reference wave shifted by a frequency Δ in respect to light used for tip and sample illumination. However, this heterodyne method can have the following shortcomings in practice: the frequency shift required for heterodyning is produced by an acousto-optic modulator (AOM) which separates the shifted beam by less than 100 mrad from the unshifted beam at its output. In such circumstances the Mach-Zender interferometer required by the method may be difficult to set up and align and the alignment of the frequency-shifted beam changes with the light wavelength. Furthermore, the AOM-s are commercially available for operation in only a few relatively narrow spectral regions, thus making the heterodyne method rather unsuitable for spectroscopic applications. Finally, the optical signal might be affected by the mechanical tip-sample interaction since the expression for the measured complex value of the signalzn˜ES,nERei(φR−φS,n+nψ) explicitly depends on the variable phase ψ of the mechanical tip oscillation.